A Reconstruction Framework for Total Generalised Variation in Photoacoustic Tomography

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from curved line artefacts and blurring, especially in case of limited angles or strong noise. Recently, there has been great interest in iterative methods using total variation, because it can deal with sharp discontinuities in photoacoustic images. However, if a heterogeneous optical density (fluence rate) is assumed, also smooth changes in the image are expected, which makes total variation unsuitable. Therefore in this work, a reconstruction model with total generalised variation is explored. This is achieved by a systematic modular framework, which gives opportunity for new relevant prior assumptions on the image. We solve the variational inverse problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator dependent preconditioning strategy. Methods are tested on 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements. As a result, acquisition time can be greatly reduced, while keeping the same reconstruction quality.